Method for determining component manufacturing tolerance based on light deviation tolerance index

Abstract

The present invention relates to the field of optical processing technology, and in particular to a method for determining component manufacturing tolerances based on a light deviation tolerance index. The method comprises adding a formal error to an ideal optical element to obtain a practical optical element; determining the incident vector of a light ray incident on the ideal optical element or the practical optical element; determining the light deviation tolerance value, and based on the incident vector, determining the ideal exit vector when the ideal optical element emits the light ray, and the practical exit vector when the practical optical element emits the light ray; calculating the angle between the ideal exit vector and the practical exit vector, and determining a constraint condition for the vector angle based on the determined light deviation tolerance value; and obtaining a constraint formula for the formal error based on the constraint condition, which is the manufacturing tolerance index. The present invention directly uses ray optics to draw first-hand conclusions, without error transfer, and is applicable to errors and curved surfaces of various scales.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing, and in particular relates to a method for determining component manufacturing tolerance based on a light deviation tolerance index. Background Art

[0002] Nowadays, there are many models for the impact of manufacturing errors on optical system imaging. If the errors are divided according to their spatial frequency, they can be divided into low-frequency errors, medium-frequency errors, and high-frequency errors. For low-frequency errors, small aberration theory can be used to calculate their impact on optical system imaging; for random high-frequency errors, scattering theory can be used to calculate their impact on optical system imaging; for periodic high-frequency errors, diffraction theory can be used to deal with them; and for those medium-frequency errors whose error scales are far different from the wavelength and the component aperture and are not suitable for the above theoretical analysis, the analysis methods are relatively limited, but there are still related studies. The paper "Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors" published in "Optics Express" proposes a PDPD method to estimate the MTF degradation range, and the paper "Effects on the OTF of MSF structures with random variations" published in "Optics Express" gives a method for analyzing OTF of turning manufacturing errors. These methods all establish a positive relationship between error and image quality. If a large number of numerical statistics are performed, it is expected that inverse error tolerance constraints can be performed.

[0003] For many large-aperture optical components, the tools available for manufacturing, such as small grinding heads, air bags, stress plates, and magnetorheological techniques, produce characteristic manufacturing errors on the millimeter scale, making the above theory inapplicable. Therefore, a general formula for millimeter-scale error tolerances is urgently needed. Summary of the Invention

[0004] In view of this, the present invention aims to provide a method for determining component manufacturing tolerances based on light deviation tolerance indicators, directly using ray optics to draw first-hand conclusions without error transmission, and applicable to errors and surfaces of various scales.

[0005] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0006] A method for determining component manufacturing tolerance based on a light deviation tolerance index, comprising:

[0007] S1: Adding form errors to the ideal optical element to obtain a real form optical element; determining the incident vector of the light incident on the ideal optical element or the real form optical element;

[0008] S2: Determine the light deviation tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits the light, and the actual form exit vector when the actual form optical element emits the light;

[0009] S3; calculating the angle between the ideal outgoing vector obtained in step S2 and the actual outgoing vector, and determining the constraint condition of the vector angle in combination with the light deviation tolerance value determined in step S2;

[0010] S4: Based on the constraint conditions obtained in step S3, a constraint formula of the formal error is obtained, and the constraint formula is the manufacturing tolerance index.

[0011] Furthermore, the process of determining the ideal outgoing vector based on the incoming vector in step S2 includes:

[0012] Calculate the normalized surface normal of an ideal optical element;

[0013] ;

[0014] in, represents the normalized surface normal of an ideal optical element, g x The x-partial derivative of the surface equation representing an ideal optical element, g y The y-partial derivative of the surface equation representing the ideal optical element;

[0015] Based on the normalized surface normal of an ideal optical element, the ideal reflection action matrix is ​​determined by the following formula:

[0016] ;

[0017] Where R represents the ideal reflection matrix, I represents the identity matrix, represents the outer product of vectors;

[0018] Based on the ideal reflection action matrix, the ideal outgoing vector is determined by the following formula:

[0019] ;

[0020] in, represents the ideal outgoing vector, represents the normalized incident vector.

[0021] Furthermore, the process of determining the actual form outgoing vector based on the incoming vector in step S2 includes:

[0022] The normalized surface normal of the actual form optical element is calculated by the following formula;

[0023] ;

[0024] in, represents the normalized surface normal of the actual form optical element, E x The x-partial derivative of the surface equation representing the actual form of the optical element, E y The y-partial derivative of the surface equation representing the actual form of the optical element;

[0025] Based on the normalized surface normal of the actual form of the optical element, the actual reflection action matrix is ​​determined by the following formula:

[0026] ;

[0027] Where M represents the actual reflection matrix and I represents the identity matrix;

[0028] Based on the actual reflection matrix, the actual form of the outgoing vector is determined by the following formula:

[0029] ;

[0030] in, Represents the actual form of the outgoing vector.

[0031] Furthermore, in step S3, the angle is obtained by the following formula:

[0032] ;

[0033] The constraints are:

[0034] cosθ(x,y)≥cosΔ(x,y);

[0035] Where θ(x,y) represents the angle, and Δ(x,y) represents the light deviation tolerance.

[0036] Furthermore, in step S4, the constraint condition is further:

[0037] ;

[0038] The constraint conditions are solved to obtain the constraint range of the formal error, which is the constraint formula.

[0039] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0040] The present invention's method for determining component manufacturing tolerances based on light deviation tolerance indicators calculates the tolerance requirements for manufacturing errors based solely on the light deviation tolerance and the form, shape, and differential of the manufacturing error. This method has strong application prospects for allocating manufacturing error tolerances in optical design. Compared to existing methods, the method provided by the present invention more directly uses ray optics to draw first-hand conclusions, eliminating error transfer. This effectively improves the accuracy of component manufacturing tolerance confirmation and expands the scope of application of optical components. Furthermore, while previous manufacturing tolerances were given using statistical indicators such as RMS, SlopeRMS, and PSD, the present invention provides a point-by-point tolerance calculation method, which, relatively speaking, provides tighter constraints on manufacturing errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0042] Figure 1 The present invention is a flowchart of a method for determining component manufacturing tolerance based on light deviation tolerance indicators according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0044] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0045] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0046] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0047] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0048] like Figure 1 As shown, the method for determining component manufacturing tolerance based on light deviation tolerance index according to the embodiment of the present invention includes:

[0049] S1: Adding a form error to an ideal optical element to obtain a real form optical element; determining an incident vector of a light ray incident on the ideal optical element or the real form optical element.

[0050] The formal error is determined in the optical design software based on the analysis scenario. According to the formal error, a corresponding error map is designed. For example, the surface of a magnetorheological polishing element will have residual characteristic mid-frequency errors, and the error map is superimposed on the surface of an ideal optical element to obtain an actual form optical element. The side of the actual form optical element on which the manufacturing error map is superimposed is the error surface. The process of obtaining the actual form optical element can be automatically implemented according to actual needs in existing optical design software, and the present invention does not impose any restrictions on this. The incident vector is determined by the way the element is used. For example, to calculate the manufacturing tolerances under different fields of view, it is necessary to calculate the incident vector corresponding to each typical field of view.

[0051] S2: Determine the light deviation tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits the light, and the actual form exit vector when the actual form optical element emits the light.

[0052] The light deviation tolerance value is given according to actual needs and is not limited in the present invention. In some embodiments, the process of determining the ideal outgoing vector based on the incident vector includes:

[0053] Calculate the normalized surface normal of an ideal optical element;

[0054] ;

[0055] in, represents the normalized surface normal of an ideal optical element, g xThe x-partial derivative of the surface equation representing an ideal optical element, g y The y-partial derivative of the surface equation representing the ideal optical element;

[0056] Based on the normalized surface normal of an ideal optical element, the ideal reflection action matrix is ​​determined by the following formula:

[0057] ;

[0058] Where R represents the ideal reflection matrix, I represents the identity matrix, represents the outer product of vectors;

[0059] Based on the ideal reflection action matrix, the ideal outgoing vector is determined by the following formula:

[0060] ;

[0061] in, represents the ideal outgoing vector, represents the normalized incident vector.

[0062] In some embodiments, the process of determining the actual form outgoing vector based on the incoming vector includes:

[0063] The normalized surface normal of the actual form optical element is calculated by the following formula;

[0064] ;

[0065] in, represents the normalized surface normal of the actual form optical element, E x The x-partial derivative of the surface equation representing the actual form of the optical element, E y The y-partial derivative of the surface equation representing the actual form of the optical element;

[0066] Based on the normalized surface normal of the actual form of the optical element, the actual reflection action matrix is ​​determined by the following formula:

[0067] ;

[0068] Where M represents the actual reflection matrix and I represents the identity matrix;

[0069] Based on the actual reflection matrix, the actual form of the outgoing vector is determined by the following formula:

[0070] ;

[0071] in, Represents the actual form of the outgoing vector.

[0072] S3; Calculate the angle between the ideal outgoing vector obtained in step S2 and the actual outgoing vector, and determine the constraint condition of the vector angle in combination with the light deviation tolerance value.

[0073] In some embodiments, the angle is obtained by the following formula:

[0074] ;

[0075] The constraints are:

[0076] cosθ(x,y)≥cosΔ(x,y);

[0077] Where θ(x,y) represents the angle, and Δ(x,y) represents the light deviation tolerance.

[0078] S4: Based on the constraint conditions obtained in step S3, a constraint formula of the formal error is obtained, and the constraint formula is the manufacturing tolerance index.

[0079] In some embodiments, the constraints are further:

[0080] ;

[0081] The constraint conditions are solved to obtain the constraint range of the formal error, which is the constraint formula.

[0082] In order to clearly illustrate the method for determining component manufacturing tolerance based on light deviation tolerance indicators described in an embodiment of the present invention, an embodiment is provided.

[0083] Example:

[0084] S1: Adding a form error to an ideal optical element to obtain a real form optical element; determining an incident vector of a light ray incident on the ideal optical element or the real form optical element.

[0085] In this embodiment, the ideal optical element is a parabolic reflector optical element in an ideal state. The surface equation of this ideal optical element is expressed as:

[0086] ;

[0087] Where f represents the focal length of the parabolic reflector optical element, specifically 500mm, and the aperture of the parabolic reflector optical element is 200mm. Correspondingly, the surface equation of the actual form optical element is expressed as:

[0088] ;

[0089] Among them, E(x,y) represents the formal error.

[0090] In this embodiment, the normalized incident vector VIn Set to V In (x,y,z)=[0,0,1] T , that is, the incident light is along [0,0,1] T The direction of incidence is on an ideal optical element or a real optical element.

[0091] S2: Determine the light deviation tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits the light, and the actual form exit vector when the actual form optical element emits the light.

[0092] In this embodiment, the light deviation tolerance value Δ(x, y) is set to 0.02 rad, that is, the deviation between the outgoing light at all positions on the actual optical element and the outgoing light at all positions on the ideal optical element does not exceed 0.02 rad.

[0093] In this embodiment, the process of determining the ideal outgoing vector based on the incoming vector includes:

[0094] Calculates the normalized surface normal of an ideal optical element ;

[0095] ;

[0096] In this embodiment, the specific calculation process is given by taking the tolerance calculation of a ray with an incident point of (x, y) = (8, 6) as an example, where (8, 6) is the position with coordinates (8, 6) inside the aperture of the parabolic reflector optical element. At this time, in the above formula, , , and then get the corresponding normalized surface normal .

[0097] Based on normalized surface normals , the ideal reflection matrix R is determined by the following formula:

[0098] .

[0099] Based on the ideal reflection matrix R, the ideal outgoing vector is determined by the following formula :

[0100] .

[0101] In this embodiment, the process of determining the actual form outgoing vector based on the incoming vector includes:

[0102] The normalized surface normal of the actual form optical element is calculated by the following formula ;

[0103] .

[0104] Based on normalized surface normals , the actual reflection matrix M is determined by the following formula:

[0105] ;

[0106] At the incident point (x, y) = (8, 6), based on the actual reflection matrix M, the actual form of the emission vector is determined by the following formula :

[0107] .

[0108] S3; Calculate the angle between the ideal outgoing vector obtained in step S2 and the actual outgoing vector, and determine the constraint condition of the vector angle in combination with the light deviation tolerance value.

[0109] Since the normalized incident vector V In The vector modulus is 1, and the actual reflection matrix M and the ideal reflection matrix R are both orthogonal matrices, so the vector modulus after transformation is 1, and then:

[0110] ;

[0111] In some embodiments, the angle is obtained by the following formula:

[0112] ;

[0113] The light deviates from the tolerance value Δ∈[0,π / 2], so the constraint condition is equivalent to:

[0114] cosθ(x,y)≥cosΔ(x,y);

[0115] The light deviation tolerance Δ(x,y)=0.02rad, cosΔ(x,y)=0.9998, and the constraints are further obtained as follows:

[0116] cosθ(x,y)≥0.9998.

[0117] S4: Based on the constraint conditions obtained in step S3, a constraint formula of the formal error is obtained, and the constraint formula is the manufacturing tolerance index.

[0118] In some embodiments, the constraints are further:

[0119] ;

[0120] Solve the constraints to obtain the constraint range of the formal error. The specific process is as follows:

[0121] ;

[0122] Substitute the above formula into the constraints and further transform it to obtain:

[0123] ;

[0124] Further we get:

[0125] ;

[0126] Further we get:

[0127] ;

[0128] We can further find that when the incident point is (x,y)=(8,6), the constraint range is:

[0129] ;

[0130] Among them, grad means to obtain the gradient, Represents the calculation modulus of a vector.

[0131] This constraint range shows that for the applied light (0,0,1), modulated by the ideal optical element, if the light emitted at (8,6) is expected to deviate by θ < 0.02rad, the gradient modulus of the error at (8,6) must be less than 2.0004×10 -4 The above constraint range is the constraint formula, which is the manufacturing tolerance index of the component at this point for this application. That is, the manufacturing tolerance index obtained by the method provided by the present invention is that if the ideal optical component is manufactured according to the requirement of applying light (0,0,1) and θ<0.02rad, then the gradient norm of the error of the actual optical component at (8,6) must be less than 2.0004×10 -4 .

[0132] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0133] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for determining component manufacturing tolerance based on light deviation tolerance indicators, characterized in that: include: S1: Add form error to the ideal optical element to obtain the actual form optical element; determining an incident vector of a light ray incident on the ideal optical element or the actual optical element; S2: Determine the light deviation tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits the light, and the actual form exit vector when the actual form optical element emits the light; S3； Calculate the angle between the ideal outgoing vector obtained in step S2 and the actual outgoing vector, and determine the constraint condition of the vector angle in combination with the light deviation tolerance value determined in step S2; S4: Based on the constraint conditions obtained in step S3, a constraint formula of the formal error is obtained, and the constraint formula is the manufacturing tolerance index.

2. The method for determining component manufacturing tolerance based on light deviation tolerance index according to claim 1, characterized in that: The process of determining the ideal outgoing vector based on the incoming vector in step S2 includes: calculating a normalized surface normal of the ideal optical element; ； in, represents the normalized surface normal of the ideal optical element, g x represents the x-partial derivative of the surface equation of the ideal optical element, g y represents the y partial derivative of the surface equation of the ideal optical element; Based on the normalized surface normal of the ideal optical element, the ideal reflection action matrix is ​​determined by the following formula: ； Wherein, R represents the ideal reflection matrix, I represents the identity matrix, represents the outer product of vectors; Based on the ideal reflection matrix, the ideal outgoing vector is determined by the following formula: ； in, represents the ideal outgoing vector, represents the normalized incident vector.

3. The method for determining component manufacturing tolerance based on light deviation tolerance index according to claim 2, characterized in that: The process of determining the actual form outgoing vector based on the incoming vector in step S2 includes: The normalized surface normal of the actual form optical element is calculated by the following formula: ； in, represents the normalized surface normal of the actual form optical element, E x The x-partial derivative of the surface equation representing the actual form of the optical element, E y a y-partial derivative of a surface equation representing the actual form optical element; Based on the normalized surface normal of the actual form optical element, the actual form reflection effect matrix is ​​determined by the following formula: ； Wherein, M represents the actual form reflection matrix, and I represents the identity matrix; Based on the actual form reflection matrix, the actual form exit vector is determined by the following formula: ； in, represents the actual form of the outgoing vector.

4. The method for determining component manufacturing tolerance based on light deviation tolerance index according to claim 3, characterized in that: In step S3, the angle is obtained by the following formula: ； The constraints are: cosθ(x,y)≥cosΔ(x,y); Wherein, θ(x, y) represents the angle, and Δ(x, y) represents the light deviation tolerance value.

5. The method for determining component manufacturing tolerance based on light deviation tolerance index according to claim 4, characterized in that: In step S4, the constraint condition is further: ； The constraint conditions are solved to obtain the constraint range of the formal error, and the constraint range is the constraint formula.

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